What do you call it when your unit does physical exercise as punishment because one soldier did something wrong?

Solution 1:

In the US Army, smoking is a general term for physical punishment, although not necessarily collective punishment, as in your example.

A Wikipedia glossary of military slang has the following entry:

smoke (verb)

(U.S. Army)

Term to describe punishment of minor offenses by means of excessive physical training.

Usage: "The drill instructor smoked me for talking back."

See U.S. Marine Corps term Thrashed

This seems to be an interesting niche preservation of an otherwise obsolete sense of the verb smoke.

According to Merriam-Webster:

smoke verb

smoked; smoking

intransitive verb

...

2 archaic: to undergo punishment: cf suffer

...although note that in the archaic sense listed here, to smoke means to be punished rather than to punish.

Disciplining an entire unit, much as you describe in your example, can be termed a smoke session, as we can see in this excerpt from a US Army document entitled Corrective Training/Corrective Action Guide for Leaders:

Leaders must exercise good judgment in the administration of corrective action. Corrective action may be applied to entire units if appropriate (correcting an entire platoon failing to show teamwork during Red Phase in a given training event by having them do five repetitions of the pushup, for example), but will be focused at the individual level whenever possible. Improper use can lead to unauthorized mass punishment or hazing. Do not refer to this type of administrative corrective measure as "smoking" or "smoke sessions;" such references give the impression that these measures are punitive or oppressive.

Urban Dictionary also has an entry for smoke session. Well, it has several. Here's the relevant one:

Smoke Session

A term originating in military recruit training, which refers to an intense physical training session, usually initiated as a form of punishment for minor infractions, where one or more individuals typically do rigorous physical activity until exhaustion and/or muscle failure.

Bro, it was a total smoke session last night after drill sergeant Wilson caught Roberts sleeping during fire watch!

Also, as mentioned in the glossary quoted above, thrashed (or perhaps thrash) is apparently a similar term in use in the US Marines:

Thrashed

(U.S. Marine Corps)

An extreme physical exercise routine ordered by DIs upon a recruit or Platoon for making a mistake which could last until complete exhaustion. Puddles of sweat are often the end result.

Solution 2:

collective punishment is the term you're looking for and it has been practised since ancient times whenever a whole group is punished for the acts of one.

Examples of collective punishment:

• During the finals of the national Dutch cup in April 2014, a few Ajax supporters interrupted the game by throwing fireworks on the field, and they inflicted severe damage to several areas of the soccer stadium. Although the damage was caused by only a handful of hooligans, the entire club was subsequently fined with €70’000, and the decision was made to ban all supporters—including the innocent majority—from attending the future games between these two teams for the following three years. www.ncbi.nlm.nih.gov

• During WWII: During the Nazi occupation of Poland, the Germans applied collective responsibility: any kind of help given to a person of Jewish faith or origin was punishable by death, and that not only for the rescuers themselves but also for their families. This was widely publicized by the Germans. During the occupation, for every German killed by a Pole, 100–400 Poles were shot in retribution. Wikipedia

• In 16th Century China: During the Ming dynasty of China, 16 palace women attempted to assassinate the Jiajing Emperor. All were sentenced to death by slow slicing. Ten members of the women's families were also beheaded, while a further 20 were enslaved and gifted to ministers. Wikipedia

Examples of collective punishment are often found in classrooms, among the military, during embargos, wars, etc.

It's worth adding that under the 1949 Geneva Conventions, collective punishment inflicted on civilian enemies is considered a war crime.

Solution 3:

In British military slang a semi-formal word used for extreme punishment of an individual is called a Beasting In general a group historically may have been "fizzed" generally subjected to "gravel bashing" (square bashing)

In Singapore a recent common term “Standby Universe” for a specific group task that may have to be repeatedly carried out from bunk to square, especially if something is stun (q.v. same link.) An individual may be subject of "Blanket Party" as a form of hazing (bullying).